Question: Simplify. Rewrite the expression in the form $x^n$. $\dfrac{x^{5}}{x^2}=$
$\begin{aligned} \dfrac{x^{5}}{x^2}&=x^{5-2} \\\\ &=x^3 \end{aligned}$ This follows from the general rule $\dfrac{x^m}{x^n}=x^{m-n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} \dfrac{x^{5}}{x^2}&=\dfrac{\overbrace{\cancel x\cdot \cancel x\cdot x\cdot x\cdot x}^\text{5 times}}{\underbrace{\cancel x\cdot \cancel x}_\text{2 times}} \\\\\\ &=\underbrace{x\cdot x\cdot x}_\text{3 times} \\\\ &=x^3 \end{aligned}$ In conclusion, $\dfrac{x^{5}}{x^2}=x^3$.